Mathematics and the Unexpected

Author: Ivar Ekeland

Publisher: University of Chicago Press

ISBN: 9780226199900

Category: Mathematics

Page: 146

View: 7209

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"Not the least unexpected thing about Mathematics and the Unexpected is that a real mathematician should write not just a literate work, but a literary one."—Ian Stewart, New Scientist "In this brief, elegant treatise, assessable to anyone who likes to think, Ivar Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project (it will snow in January) but particulars are practically impossible (it will snow from 2 p.m. to 5 p.m. on the 21st)."—Village Voice
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The Best of All Possible Worlds

Mathematics and Destiny

Author: Ivar Ekeland

Publisher: University of Chicago Press

ISBN: 0226199959

Category: Mathematics

Page: 207

View: 4301

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Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer. This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today. Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition—one that will be essential reading for popular-science buffs and historians of science alike.
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The Broken Dice, and Other Mathematical Tales of Chance

Author: Ivar Ekeland

Publisher: University of Chicago Press

ISBN: 9780226199924

Category: Mathematics

Page: 190

View: 7073

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Ivar Ekeland extends his consideration of the catastrophe theory of the universe begun in his widely acclaimed Mathematics and the Unexpected, by drawing on rich literary sources, particularly the Norse saga of Saint Olaf, and such current topics as chaos theory, information theory, and particle physics. "Ivar Ekeland gained a large and enthusiastic following with Mathematics and the Unexpected, a brilliant and charming exposition of fundamental new discoveries in the theory of dynamical systems. The Broken Dice continues the same theme, and in the same elegant, seemingly effortless style, but focuses more closely on the implications of those discoveries for the rest of human culture. What are chance and probability? How has our thinking about them been changed by the discovery of chaos? What are all of these concepts good for? . . . Ah, but, I mustn't give the game away, any more than I should if I were reviewing a detective novel. And this is just as gripping a tale. . . . Beg, borrow, or preferably buy a copy. . . . I guarantee you won't be disappointed."—Ian Stewart, Science
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Mathematics and the Aesthetic

New Approaches to an Ancient Affinity

Author: Nathalie Sinclair,William Higginson

Publisher: Springer Science & Business Media

ISBN: 9780387381459

Category: Mathematics

Page: 288

View: 4147

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This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.
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The Weil Conjectures

On Maths and the Pursuit of the Unknown

Author: Karen Olsson

Publisher: Bloomsbury Publishing

ISBN: 1526607557

Category: Biography & Autobiography

Page: 224

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'A wonderful book ... Reading it is akin to kicking a can along the road of higher learning' Patti Smith Simone Weil: famous French philosopher, writer, political activist, mystic – and sister to André, one of the most influential mathematicians of the twentieth century. For Karen Olsson, who studied mathematics at Harvard only to turn to writing as a vocation, the lives and obsessions of these two extraordinary siblings returned her to the intellectual passions of her youth. When Olsson got hold of the 1940 letters between Simone and André, she discovered that André's pursuit of his studies became increasingly incomprehensible to his sister, leading to Simone directly questioning him about the value of such rarefied knowledge as it applied to the lived experience. Struck by this conflict, Olsson revisits her own time at university, how she came to be consumed by mathematics, and the unexpected similarities that can be found between two seemingly opposed subjects. At the core of the book lies her curiosity about the inception of creative thought - that flash of insight - experienced by writers and mathematicians alike. A rare work of non-fiction that intricately weaves together biography, memoir, history and philosophy, and written with prose of precision and poetic lucidity, The Weil Conjectures is nothing short of a complete seduction in the art of mathematics, and the mysterious nature of scientific and creative thought.
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Mathematical Curiosities

A Treasure Trove of Unexpected Entertainments

Author: Alfred S. Posamentier,Ingmar Lehmann

Publisher: Prometheus Books

ISBN: 1616149329

Category: Mathematics

Page: 382

View: 3241

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An innovative and appealing way for the layperson to develop math skills--while actually enjoying it Most people agree that math is important, but few would say it's fun. This book will show you that the subject you learned to hate in high school can be as entertaining as a witty remark, as engrossing as the mystery novel you can't put down--in short, fun! As veteran math educators Posamentier and Lehmann demonstrate, when you realize that doing math can be enjoyable, you open a door into a world of unexpected insights while learning an important skill. The authors illustrate the point with many easily understandable examples. One of these is what mathematicians call the "Ruth-Aaron pair" (714 and 715), named after the respective career home runs of Babe Ruth and Hank Aaron. These two consecutive integers contain a host of interesting features, one of which is that their prime factors when added together have the same sum. The authors also explore the unusual aspects of such numbers as 11 and 18, which have intriguing properties usually overlooked by standard math curriculums. And to make you a better all-around problem solver, a variety of problems is presented that appear simple but have surprisingly clever solutions. If math has frustrated you over the years, this delightful approach will teach you many things you thought were beyond your reach, while conveying the key message that math can and should be anything but boring.
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Unexpected Links between Egyptian and Babylonian Mathematics

Author: Jöran Friberg

Publisher: World Scientific

ISBN: 9814480401

Category: Science

Page: 308

View: 9088

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Mesopotamian mathematics is known from a great number of cuneiform texts, most of them Old Babylonian, some Late Babylonian or pre-Old-Babylonian, and has been intensively studied during the last couple of decades. In contrast to this Egyptian mathematics is known from only a small number of papyrus texts, and the few books and papers that have been written about Egyptian mathematical papyri have mostly reiterated the same old presentations and interpretations of the texts. In this book, it is shown that the methods developed by the author for the close study of mathematical cuneiform texts can also be successfully applied to all kinds of Egyptian mathematical texts, hieratic, demotic, or Greek-Egyptian. At the same time, comparisons of a large number of individual Egyptian mathematical exercises with Babylonian parallels yield many new insights into the nature of Egyptian mathematics and show that Egyptian and Babylonian mathematics display greater similarities than expected. Contents:Two Curious Mathematical Cuneiform Texts from Old Babylonian MariHieratic Mathematical Papyri and Cuneiform Mathematical TextsDemotic Mathematical Papyri and Cuneiform Mathematical TextsGreek-Egyptian Mathematical Documents and Cuneiform Mathematical Texts Readership: Mathematicians, historians of science, egyptologists and assyriologists. Keywords:Babylonian Mathematics;Egyptian Mathematics;Greek Mathematics;Mathematical Cuneiform Texts;Mathematical Papyri;Ancient Mathematics;Early Mathematics;History of Mathematics;Demotic Texts;Hieratic TextsKey Features:Extensive surveys of known Egyptian mathematical textsNew interpretations of particularly difficult Egyptian or Babylonian mathematical exercisesMany detailed diagrams and figures, using computer-aided methods of presentationsInteresting observations of experiments with new ways of representing fractions in demotic and Greek-Egyptian mathematical texts
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Mathematics and the Body

Material Entanglements in the Classroom

Author: Elizabeth de Freitas,Nathalie Sinclair

Publisher: Cambridge University Press

ISBN: 1107039487

Category: Education

Page: 312

View: 9020

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This book expands the landscape of research in mathematics education by analyzing how the body influences mathematical thinking.
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Financial Econometrics, Mathematics and Statistics

Theory, Method and Application

Author: Cheng-Few Lee,Hong-Yi Chen,John Lee

Publisher: Springer

ISBN: 1493994298

Category: Business & Economics

Page: 655

View: 6217

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This rigorous textbook introduces graduate students to the principles of econometrics and statistics with a focus on methods and applications in financial research. Financial Econometrics, Mathematics, and Statistics introduces tools and methods important for both finance and accounting that assist with asset pricing, corporate finance, options and futures, and conducting financial accounting research. Divided into four parts, the text begins with topics related to regression and financial econometrics. Subsequent sections describe time-series analyses; the role of binomial, multi-nomial, and log normal distributions in option pricing models; and the application of statistics analyses to risk management. The real-world applications and problems offer students a unique insight into such topics as heteroskedasticity, regression, simultaneous equation models, panel data analysis, time series analysis, and generalized method of moments. Written by leading academics in the quantitative finance field, allows readers to implement the principles behind financial econometrics and statistics through real-world applications and problem sets. This textbook will appeal to a less-served market of upper-undergraduate and graduate students in finance, economics, and statistics. ​
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Fluke

The Math and Myth of Coincidence

Author: Joseph Mazur

Publisher: Basic Books

ISBN: 0465040004

Category: Mathematics

Page: 288

View: 6290

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A mathematical guide to understanding why life can seem to be one big coincidence—and why the odds of just about everything are better than we would think
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